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1. Combine 1 tablespoon oil, 1 teaspoon garlic, 1/4 teaspoon salt, and 1/8 teaspoon pepper in medium bowl. Add shrimp, toss to coat, and refrigerate until ready to use.
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2. Place reserved shrimp shells, water, chicken broth, and bay leaf in medium bowl. Cover and microwave until liquid is hot and shells have turned pink, about 6 minutes. Set aside until ready to use.
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3. Toss spaghettini and 2 teaspoons oil in broiler-safe 12-inch skillet until spaghettini is evenly coated. Toast spaghettini over medium-high heat, stirring frequently, until browned and nutty in aroma (spaghettini should be color of peanut butter), 6 to 10 minutes. Transfer spaghettini to bowl. Wipe out skillet with paper towel.
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4. Heat remaining 2 tablespoons oil in now-empty skillet over medium-high heat until shimmering. Add onion and 1/4 teaspoon salt; cook, stirring frequently, until onion is softened and beginning to brown around edges, 4 to 6 minutes. Add tomatoes and cook, stirring occasionally, until mixture is thick, dry, and slightly darkened in color, 4 to 6 minutes. Reduce heat to medium and add remaining garlic, paprika, smoked paprika, and anchovy paste. Cook until fragrant, about 1 1/2 minutes. Add spaghettini and stir to combine. Adjust oven rack 5 to 6 inches from broiler element and heat broiler.
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5. Pour broth through fine-mesh strainer into skillet. Add wine, 1/4 teaspoon salt, and 1/2 teaspoon pepper and stir well. Increase heat to medium-high and bring to simmer. Cook uncovered, stirring occasionally, until liquid is slightly thickened and spaghettini is just tender, 8 to 10 minutes. Scatter shrimp over spaghettini and stir shrimp into spaghettini to partially submerge. Transfer skillet to oven and broil until shrimp are opaque and surface of spaghettini is dry with crisped, browned spots, 5 to 7 minutes. Remove from oven and let stand, uncovered, for 5 minutes. Sprinkle with parsley and serve immediately, passing lemon wedges separately.
